Study On Robust Control For Uncertain Singular Systems

Because of the changing of running environment and other unmeasurable disturbances, it is impossible to obtain the exact mathematics model of practical systems. The difference usually can be described as the uncertainties. Moreover, time delays are frequently encountered in a variety of practical systems. Uncertainties and time delays are often sources of instability and deterioration of system performances. The robust control theory for uncertain time-delay systems is mature. But when the system takes on non-full states, which include fast and slow states, it is named as singular system. Singular systems appear naturally in the study of some naturally occurring systems than regular ones, e.g. in electric power systems, biochemical process, nuclear reactor, airplane and rocket systems. The solution of singular system is not unique and impulse-free, which is not existing in regular systems. Therefore, the study on robust control for uncertain singular systems with delays is important both in theory and in practice.The robust control problem for uncertain singular systems with delays is studied in this dissertation. Based on integral inequality ( or finite sum inequality), Barblat lemma, through using linear matrix inequality (LMI), this dissertation tackles the robust stability problem,robust stabilization problem and robust H_∞control problem for linear singular systems with time delays. The problems of robust stability and reliable robust H_∞tracking control for nonlinear singular systems are also studied. The major contributions of this dissertation are as follows:(1) Based on integral inequality ( or finite sum inequality), an LMI approach to the robust stability, robust stabilization and robust H_∞control of uncertain continuous-time and discrete-time linear singular systems with time-varying delay is developed. Some delay-dependent conditions are obtained and the explicit expression of the desired state-feedback control laws are also given.(2) The problems of robust stability and robust stabilization for a class of norm-bounded uncertain linear continuous-time singular system with discrete and distributed time delays are studied. By introducing a new input-output model, an input-output approach, which reduces the stability analysis of the uncertain system to the analysis of a class of systems with the same nominal part but with additional inputs and outputs, is applied. Based on the definition of input-output stability, some sufficient and necessary conditions are obtained for the concerned singular systems. It makes up the shortcoming of the existing results.(3) The absolute stability problem of a class of norm-bounded uncertain Lur'e singular systems with various time delays is studied. The nonlinear terms are constrained in the finite Hurwitz sector. Two types of time-delay are discussed: time-invariant delay and time-varying delay, and time-varying delay includes (I) continuous but not differential and (II) continuous and differential. Moreover, the relationship between these two cases is also explained.(4) The robust stability problem of a class of neutral singular system with nonlinear parameter perturbations is studied. Some discrete-delay-dependent/neutral-delay-dependent, discrete-delay-dependent / neutral-delay-independent, delay-independent conditions are obtained for different cases. The result shows that norm-bounded uncertainties are the special cases for such nonlinear parameter perturbations.(5) The problem of reliable robust H_∞tracking control for a class of uncertain Lur'e singular systems is studied. A practical and general failure model of actuator and sensor is considered by using convex polytopic uncertainties to describe control surface impairment failures. A sufficient condition of reliable robust H_∞tracking control is presented for the case of actuator, sensor and control surface failures in terms of Linear Matrix Inequalities ( LMIs ). The resulting control systems are reliable in that they guarantee closed-loop system robust stability with H_∞performance and the output tracking the reference signal without steady-state error when all control components are operational as well as when some control components experience failures.The dissertation concludes with a perspective of future research on robust control on singular systems.